Can P0420 cause no power, rough idle, improper shifts, or limp mode?

Hello, P0420 itself indicates catalyst inefficiency has been identified. This is likely caused by an ineffective catalytic converter being utilized. You may have replaced one that was spent with one that isn't up to the task of burning the contaminants and exhaust gases effectively enough. This would cause the code to return. Then you mention "gutted the converter" and I'm not sure what that means. Doesn't sound positive though. Sounds like you've made a tremendous effort to repair multiple areas of the vehicle. And it seems like much of it is educated guesses and consulting someone at your local Nissan dealership -- which isn't really going to be as effective as being a factory trained technician using proper diagnostic equipment and referring to workshop manuals and wiring diagrams. It is too much, too convoluted and has had too much done already to make any valid suggestion here. So I'll advise to seek guidance at a local shop near you, where all work performed to date can be evaluated hands on and advice can be given moving forward in the best way. Use this link to find some shops near you that can help with your concern: www.repairpal.com/repair-shops